The Taoiseach has said there is still an opportunity to avoid a general election.
It comes after Fianna Fáil tabled a motion of no confidence in the Tánaiste Frances Fitzgerald.
The motion will be debated in the Dáil next Tuesday. If it is passed, the party will be in breach of the confidence and supply agreement that is propping up the minority-led Fine Gael government - triggering a general election.
Should the Tánaiste resign or be removed from her position in the meantime, the crisis could be avoided.
However, the Fine Gael parliamentary party on Thursday voted unanimously to support her.
"I'm not going to be rushing to the Park"
The Taoiseach spoke to RTÉ News this evening, after what he described as a 'good meeting' with Fianna Fáil leader Micheál Martin.
The two party leaders are due to meet again tomorrow.
Mr Varadkar admitted we will be into an election if a no confidence motion passes, but continued to express his support for Minister Fitzgerald.
He explained: "We still have an opportunity over the next couple of days and over the to avoid a general election.
"I don't want there to be a general election... I don't believe Micheál Martin wants one either, by the way."
He said he will not be seeking Frances Ftizgerald's resignation, claiming that the case against her is 'very, very flimsy'.
He suggested: "I don't believe the decapitation of the Tánaiste based on trumped up charges is fair - especially when in only a few weeks time the Tribunal the Oireachtas set up to look into these matters is going to do exactly that.
He also observed that removing Minister Fitzgerald as Tánaiste would mean "throwing a good woman under the bus for political expediency to save myself and my own Government - and that would be the wrong thing to do."
If an election does happen, he said it would be better to have it before Christmas to better facilitate the ongoing Brexit talks in Europe.
However, he stressed: "I'm not going to be rushing to the Park over the weekend to dissolve the Dáil. If this Government falls, it will be because Fianna Fáil and Sinn Féin and others combined to vote no confidence in a member of the Government."
"We all need to cop on to ourselves"
Fine Gael Minister Regina Doherty says nobody wants to go to the polls.
"There's nobody in their right mind in this country would want, or think, that people in this country want an election or deserve an election.
"We all need to cop on to ourselves and go back to the table and sort this mess out once and for all.
"Everything can be resolved through conciliation and mediation - let's sit at the table and resolve these issues".
Fianna Fáil finance spokesman Michael McGrath says it is now up to Mr Varadkar and Ms Fitzgerald.
"We still think an election can be avoided - that is our genuine aspiration - but the ball is very much in the Government's court.
"It is now a matter for the Taoiseach and the the Tánaiste to consider and reflect on over the weekend".
"I have ruled out any prospect of going into government with SF. The FF party took a clear decision prior to the last election, it continues in advance of the next election, and again in its aftermath" - @MichealMartinTD #TodaySOR https://t.co/ujwBmr5cLP
— Fianna Fáil (@fiannafailparty) November 24, 2017
Senior members of Sinn Féin earlier attended a special meeting to discuss the potential vote.
Speaking afterwards, the party's finance spokesman Pearse Doherty says Mary Lou McDonald will lead the party into any potential election.
"Mary Lou McDonald will lead our campaign in the election, if there is to be an election.
"But that is a decision for Leo Varadkar.
"What we have very clearly is a motion of no confidence in the Tánaiste - we want to see the Tánasite go, and is up to Leo now whether he wants to walk this State into a general election".
Mary-Lou McDonald will lead Sinn Fein into the next election when it happens but Pearse Doherty is calling on Frances Fitzgerald to resign pic.twitter.com/iJNpO5aunQ
— Juliette Gash (@JulietteGash) November 24, 2017
The party's president Gerry Adams announced last week that he would not be standing for a Dáil seat at the next election.
While the Independent Alliance say they have confidence in Ms Fitzgerald "100%", and are calling on Fine Gael and Fianna Fáil to pull back from the brink of an election.
— Juliette Gash (@JulietteGash) November 24, 2017
And following a party meeting this morning, Labour said it is on 'election footing' - but suggested there is still an opportunity for Fine Gael to 'reflect on the situation'.
Party leader Brendan Howlin explained: "If the Tánaiste resigns, the threat of an immediate election could pass, allowing the Taoiseach to focus on Brexit and other matters, as Fine Gael have made clear they want to. But if they are determined not to budge, then so be it.
“It seems likely now that an election will be called over the next week. And we are ready for it."
He added that the party had "never had confidence" in the current Government, arguing that they have "lurched from one crisis to the next".
The Green Party, in contrast, called on Fianna Fáil and Sinn Féin to postpone their motions of no confidence in Minister Fitzgerald until the New Year.
Leader Eamon Ryan said: “Whatever the position of each party on the Garda whistle-blower controversy, everyone will agree that an election before Christmas is not in the national interest.
“We do not want an election in the middle of the critical Brexit talks, and postponing the motions until the New Year would allow the important work of the Joint Committee on the 8th Amendment to be completed, and allow time to get the Finance, FEMPI, and Social Welfare bills over the line."
Opposition parties have seized on Frances Fitzgerald’s handling of an email in May 2015 which alluded to a garda strategy to discredit Maurice McCabe.
Minister Fitzgerald has continually insisted she had no knowledge of any alleged strategy until 2016, when it entered the public domain. She has said does not remember the email, adding that it would have been “inappropriate and improper” for her to have intervened in any case.
The Sinn Féin motion handed in on Thursday reads:
"This House, declares that Dáil Éireann has no confidence in the Tánaiste Frances Fitzgerald, and calls on her to resign from the Position of Tánaiste, and from the position of Minister of Business, Enterprise and Innovation forthwith."
Sinn Féin TD David Cullinane said there is a simple way to resolve the matter, insisting that if the Tánaiste does not resign then it "is open to the Taoiseach to sack her."